A thin uniform rod of length 2 m, cross sectional area ' A ' and density ' d ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity ω. If value of ω in terms of its rotational kinetic energy E is √(α Ad / Ad ) then value of α is

Question

A thin uniform rod of length 2 m, cross sectional area ' A ' and density ' d ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity ω. If value of ω in terms of its rotational kinetic energy E is √(α Ad / Ad ) then value of α is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

( KE ) text Rotational =(1/2) I ω2= E E =(1/2) ( m ℓ2/12) ω2 E =(1/2) ( dA ℓ3/12) ω2 E =( dA (2)3/24) ω2 √(3 E / dA )=ω α=3

Q. A thin uniform rod of length 2m, cross sectional area ' A ' and density ' d ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity ω. If value of ω in terms of its rotational kinetic energy E is AdαAd​​ then value of α is _____

(KE)Rotational ​=21​Iω2=E E=21​12mℓ2​ω2 E=21​12dAℓ3​ω2 E=24dA(2)3​ω2 dA3E​​=ω α=3

$(K E)_{Rotational} = \frac{1}{2} I ω^{2} = E$
$E = \frac{1}{2} \frac{m ℓ ^{2}}{12} ω^{2}$
$E = \frac{1}{2} \frac{d A ℓ ^{3}}{12} ω^{2}$
$E = \frac{d A ( 2 ) ^{3}}{24} ω^{2}$
$\frac{3 E}{d A} = ω$
$α = 3$